Its always a relief to get the doctor's "okay" for a strenous sport like running. When I started back running a few years ago (after taking a long hiatus) I also had a stress test and the doctor told me "run and train all you want, you're good to go". It was music to my ears!
As far as the anemia, if could definitely affect your running even though you don't notice it in your day to day activities. I donated blood a couple of years ago and afterwards felt perfectly fine. I didn't notice any difference in my regular activities but for a few weeks afterwards I felt SOOOO fatigued when I ran. Not out of breath, like you're saying, but just dragged out and listless. So yeah, anemia could be a factor. Hope you get that resolved!